5. Consider the force field F = (xy)i + (x −y)j and C, the straight line from the point (-1,2) to (3,3). (a) Find a parameterization of the straight line C. Show your process for this. Include the range of values of the parameter in your final answer. I (b) Express the work done by the field F along the line C as a line integral. Then convert that line integral into a single-variable integral.

Q: Draw the slope field (direction field) for the following DE: y'=y-t

A: Given DE is Make table as follows:…

Q: Sketch a direction field for the equation y'= 2y(1-y) by hand. Then use that and sketch a few…

A:

Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A:

Q: Find the work done by F over the curve in the direction of increasing t. F = 4zi + 4xj + 4yk, r(t) =…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A:

Q: 2) Let r(t) = (t, t² , e'). Find an equation for the unit tangent vector T(t).

A:

Q: Sex. (x+y)ds where C is the straight-line segment x = 3t, y = (3-3t), z = 0 from C (0,3,0) to…

A:

Q: Find the potential function f for the field F = 6x i + 6y j + 7z k. A general expression for the…

A: Note: As you have posted multiple question but I will answer first question according to the…

Q: Compute the work done by the force F = (sin(x + y), xy, x²z) in moving an object along the…

A: Given information:Force vector in Newtons.Initial point .Intermediate point .Final point .To find:…

Q: Calculate the work done by the force field on the particle.

A: